{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Created by Tirthajyoti Sarkar, Ph.D., Jan 2018"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean-shift Clustering Technique\n",
    "\n",
    "Mean-shift clustering aims to discover blobs in a smooth density of samples. It is a centroid based algorithm, which works by updating candidates for centroids to be the mean of the points within a given region. These candidates are then filtered in a post-processing stage to eliminate near-duplicates to form the final set of centroids.\n",
    "\n",
    "Given a candidate centroid $x_i$ for iteration $t$, the candidate is updated according to the following equation:\n",
    "\n",
    "$$x_i^{t+1} = x_i^t + m(x_i^t)$$\n",
    "\n",
    "Where $N(x_i)$ is the neighborhood of samples within a given distance around $x_i$ and $m$ is the mean shift vector that is computed for each centroid that points towards a region of the maximum increase in the density of points. This is computed using the following equation, effectively updating a centroid to be the mean of the samples within its neighborhood:\n",
    "\n",
    "$$m(x_i) = \\frac{\\sum_{x_j \\in N(x_i)}K(x_j - x_i)x_j}{\\sum_{x_j \\in N(x_i)}K(x_j - x_i)}$$\n",
    "\n",
    "**The algorithm automatically sets the number of clusters, instead of relying on a parameter bandwidth, which dictates the size of the region to search through**. This parameter can be set manually, but can be estimated using the provided estimate_bandwidth function, which is called if the bandwidth is not set.\n",
    "\n",
    "**The algorithm is not highly scalable, as it requires multiple nearest neighbor searches** during the execution of the algorithm. The algorithm is guaranteed to converge, however the algorithm will stop iterating when the change in centroids is small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make the synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import MeanShift\n",
    "from sklearn import metrics\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "\n",
    "# Generate sample data\n",
    "centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "X, labels_true = make_blobs(n_samples=300, centers=centers, cluster_std=0.4,random_state=101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(300, 2)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RZkuy/Gll6sif3nPfg9y34CXeHF3DbdfDjoN6ftqsEn32/KU8cEk9fuQUfHAS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\nJxlMwPDNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b841f43cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(X[:,0],X[:,1],edgecolors='k',c='orange',s=75)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "ms_model = MeanShift().fit(X)\n",
    "cluster_centers = ms_model.cluster_centers_\n",
    "labels = ms_model.labels_\n",
    "n_clusters = len(cluster_centers)\n",
    "labels = ms_model.labels_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Number of detected clusters and their centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of clusters detected by the algorithm: 3\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of clusters detected by the algorithm:\", n_clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster centers detected at:\n",
      "\n",
      " [[ 0.9931698   1.05074234]\n",
      " [ 1.09954715 -1.09294823]\n",
      " [-0.99420039 -0.96765319]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Cluster centers detected at:\\n\\n\", cluster_centers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9uQ4UIWRZO7FzXV6DehsMBrKysmjevPlxB+xDXnzlRapCStmj2YZT1s00l1JS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\nz8GDBwl+dAn3YnKKuL7sIyzkaMS6X63JSLnPtm3bsr3n8uXLNGxQi2q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eBdOns2LpUoOJ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\ncNM2MzMrhJu2mZlZIdy0zczMCvEHcoEVQ7Q04XIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b841e83438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(X[:,0],X[:,1],edgecolors='k',c=ms_model.labels_,s=75)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Homogeneity\n",
    "\n",
    "Homogeneity metric of a cluster labeling given a ground truth.\n",
    "\n",
    "A clustering result satisfies homogeneity if all of its clusters contain only data points which are members of a single class. This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Homogeneity score: 0.940507302233\n"
     ]
    }
   ],
   "source": [
    "print (\"Homogeneity score:\", metrics.homogeneity_score(labels_true,labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Completeness\n",
    "\n",
    "Completeness metric of a cluster labeling given a ground truth.\n",
    "\n",
    "A clustering result satisfies completeness if all the data points that are members of a given class are elements of the same cluster. This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Completeness score: 0.940507302233\n"
     ]
    }
   ],
   "source": [
    "print(\"Completeness score:\",metrics.completeness_score(labels_true,labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time complexity and model quality as the data size grows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import time\n",
    "from tqdm import tqdm "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████████████| 12/12 [01:04<00:00,  5.39s/it]\n"
     ]
    }
   ],
   "source": [
    "n_samples = [10,20,50,100,200,500,1000,2000,3000,5000,7500,10000]\n",
    "centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "t_ms = []\n",
    "homo_ms=[]\n",
    "complete_ms=[]\n",
    "\n",
    "for i in tqdm(n_samples):\n",
    "    X,labels_true = make_blobs(n_samples=i, centers=centers, cluster_std=0.4,random_state=101)\n",
    "    t1 = time.time()\n",
    "    ms_model = MeanShift().fit(X)\n",
    "    t2=time.time()\n",
    "    t_ms.append(t2-t1)\n",
    "    homo_ms.append(metrics.homogeneity_score(labels_true,ms_model.labels_))\n",
    "    complete_ms.append(metrics.completeness_score(labels_true,ms_model.labels_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZbYiknQ7vi4iI1BBK+iIiIjWEkr6IiEgNoaQvIiJSQyjpi4iI1BBK+iIiIjWEkr6IiEic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\n9M3MzErE/wMpblfsWae7BQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b841cc8fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Time complexity of Mean Shift\\n\",fontsize=20)\n",
    "plt.scatter(n_samples,t_ms,edgecolors='k',c='green',s=100)\n",
    "plt.plot(n_samples,t_ms,'k--',lw=3)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Number of samples\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Time taken for model (sec)\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1CkcddRQJCe4Oo/rSHqaiI6VVij0WS7B9ZsD2f0l3/gpw0JbzSUpKYsyYMRVO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b841c3ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Homogeneity score with data set size\\n\",fontsize=20)\n",
    "plt.scatter(n_samples,homo_ms,edgecolors='k',c='green',s=100)\n",
    "plt.plot(n_samples,homo_ms,'k--',lw=3)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Number of samples\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Homogeneity score\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6WGiF69QYbIe3LJxNwCgRSVTVkndzH0q76JVaC6zE9Yloi5ul4E0ROUlVP6xu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\nJicLZmZmlun/ARMRKxWIQUAgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b841c33668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Completeness score with data set size\\n\",fontsize=20)\n",
    "plt.scatter(n_samples,complete_ms,edgecolors='k',c='green',s=100)\n",
    "plt.plot(n_samples,complete_ms,'k--',lw=3)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Number of samples\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Completeness score\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How well the cluster detection works in the presence of noise?\n",
    "\n",
    "Create data sets with varying degree of noise std. dev and run the model to detect clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noise = [0.01,0.05,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.25,1.5,1.75,2.0]\n",
    "n_clusters = []\n",
    "for i in noise:\n",
    "    centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "    X, labels_true = make_blobs(n_samples=200, centers=centers, cluster_std=i,random_state=101)\n",
    "    ms_model=MeanShift().fit(X)\n",
    "    n_clusters.append(len(ms_model.cluster_centers_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Detected number of clusters: [3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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X3pvB8UTKz+A4IOvT3Kz8M8D5pIR3BkX/D7I6u5I+H68WvI8LYz+S92Z8fZH0o+afK70W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\nmZX6P+MDAYNs85KQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b8375e9518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Detected number of clusters:\",n_clusters)\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Cluster detection with noisy data\\n\",fontsize=20)\n",
    "plt.scatter(noise,n_clusters,edgecolors='k',c='green',s=100)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Noise std.dev\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Number of clusters detected\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** We see that the cluster detection works well up to a certain level of noise std. dev, after which the mean of the blobs shifts to the overall centroid and the number of detected clusters tends to 1**"
   ]
  }
 ],
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